Habitat fragmentation is expected to disrupt dispersal, and thus we explored how patch metrics of landscape structure, such as percolation thresholds used to define landscape connectivity, corresponded with dispersal success on neutral landscapes. We simulated dispersal as either a purely random process (random direction and random step lengths) or as an area-limited random walk (random direction, but movement limited to an adjacent cell at each dispersal step) and quantified dispersal success for 1000 individuals on random and fractal landscape maps across a range of habitat abundance and fragmentation. Dispersal success increased with the number of cells a disperser could search (m), but poor dispersers (m<5) searching via area-limited dispersal on fractal landscapes were more successful at locating suitable habitat than random dispersers on either random or fractal landscapes. Dispersal success was enhanced on fractal landscapes relative to random ones because of the greater spatial contagion of habitat. Dispersal success decreased proportionate to habitat loss for poor dispersers (m=1) on random landscapes, but exhibited an abrupt threshold at low levels of habitat abundance (p<0.1) for area-limited dispersers (m<10) on fractal landscapes. Conventional metrics of patch structure, including percolation, did not exhibit threshold behavior in the region of the dispersal threshold. A lacunarity analysis of the gap structure of landscape patterns, however, revealed a strong threshold in the variability of gap sizes at low levels of habitat abundance (p<0.1) in fractal landscapes, the same region in which abrupt declines in dispersal success were observed. The interpatch distances or gaps across which dispersers must move in search of suitable habitat should influence dispersal success, and our results suggest that there is a critical gap-size structure to fractal landscapes that interferes with the ability of dispersers to locate suitable habitat when habitat is rare. We suggest that the gap structure of landscapes is a more important determinant of dispersal than patch structure, although both are ultimately required to predict the ecological consequences of habitat fragmentation.